Monday, Vice President Dick Cheney was hospitalized in Washington after complaining of repeated bouts of "chest discomfort." Doctors at George Washington University Hospital released the vice president Tuesday morning after performing an angioplasty  a common procedure used to clear out blocked arteries.

While the White House took a characteristically sunny view of Cheney's health, some Washington insiders are reportedly starting to whisper about substitutes for Bush's right-hand man, who has suffered four heart attacks in the last 25 years, the first when he was just 37. The specter of replacing Cheney looms large over the White House, says TIME national reporter Mitch Frank, because Cheney plays such a critical role in the administration.

TIME.com: Cheney apparently shoulders a great deal of responsibility in this administration, and works spectacularly hard. Will this latest health scare slow him down?

Frank: Probably not. Cheney has always been a very hard worker, and it would be really difficult to convince him to cut back. This is the guy who not only sells the President's tax plan to Congress, but who also tackles the conservative media and sells the plan there, while Bush appears on mainstream channels. At this point, selling the plan to Congress is essentially the most important job, and Cheney knows it. The early word is that Bush will have trouble in the Senate  some moderate Democrats are reportedly offended by the way House Republicans just pushed the plan right through on their side. Many Democrats are saying, "Look, you haven't given us a budget yet, and you're asking us to pass a tax cut?"

What would happen if Cheney's health forced him to step down?

Frank: Nobody's actually talking about this right now, but the White House has to wonder if they're putting the man's health at risk by having him work so hard. At the same time, you can't force him to stop working. But considering how hard Cheney does work, the administration would pay a serious price if the vice president were to leave  and possibly be forced to redesign their entire infrastructure.

If, for whatever reason, Bush did have to find a replacement for Cheney, it would be like running a vice presidential search committee all over again.
The President would pick Cheney's successor, and the Congress would have to approve the choice. The problem with these replacements is the ugly spectacle of having the person first in line to the presidency not elected to the office by the American people.

Some pundits and papers are accusing the White House of spinning Cheney's health problems into an improbably happy picture. Are the White House spin doctors out of control?

Frank: They're in a tough spot; there's really no good message they can give on this. Cheney has heart disease. And even if this guy cuts down on his schedule, he will still have health problems.

In retrospect, what the White House should have done is issue a statement right away so it didn't look like CNN was breaking the story.